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Contact hamiltonians distinguishing locally certain Goursat systems

Piotr Mormul (2000)

Banach Center Publications

For the first time in dimension 9, the Goursat distributions are not locally smoothly classified by their small growth vector at a point. As shown in [M1], in dimension 9 of the underlying manifold 93 different local behaviours are possible and four irregular pairs of them have coinciding small growth vectors. In the present paper we distinguish geometrically objects in three of those pairs. Smooth functions in three variables - contact hamiltonians in the terminology of Arnold, [A] - help to do...

Contact Quantization: Quantum Mechanics = Parallel transport

G. Herczeg, E. Latini, Andrew Waldron (2018)

Archivum Mathematicum

Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and momenta as points on an underlying phase-spacetime and reduces classical mechanics to contact topology. Contact quantization describes quantum dynamics in terms of parallel transport for a flat connection; the ultimate goal being to also handle quantum systems in terms...

Formes de contact ayant le même champ de Reeb

Aggoun, Saad (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 37J55, 53D10, 53D17, 53D35.In this paper, we study contact forms on a 3-manifold having a common Reeb vector field R. The main result is that when the contact forms induce the same orientation, they are diffeomorphic.

g -natural metrics of constant curvature on unit tangent sphere bundles

M. T. K. Abbassi, Giovanni Calvaruso (2012)

Archivum Mathematicum

We completely classify Riemannian g -natural metrics of constant sectional curvature on the unit tangent sphere bundle T 1 M of a Riemannian manifold ( M , g ) . Since the base manifold M turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian g -natural metric on the unit tangent sphere bundle of a Riemannian surface.

Generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds

Amalendu Ghosh (2015)

Annales Polonici Mathematici

We consider generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds. First, we prove that a complete Sasakian manifold M admitting a generalized m-quasi-Einstein metric is compact and isometric to the unit sphere S 2 n + 1 . Next, we generalize this to complete K-contact manifolds with m ≠ 1.

Handle attaching in symplectic homology and the Chord Conjecture

Kai Cieliebak (2002)

Journal of the European Mathematical Society

Arnold conjectured that every Legendrian knot in the standard contact structure on the 3-sphere possesses a haracteristic chord with respect to any contact form. I confirm this conjecture if the know has Thurston-Bennequin invariant 1 . More generally, existence of chords is proved for a standard Legendrian unknot on the boundary of a subcritical Stein manifold of any dimension. There is also a multiplicity result which implies in some situations existence of infinitely many chords. The proof relies...

Infinitesimal automorphisms and deformations of parabolic geometries

Andreas Čap (2008)

Journal of the European Mathematical Society

We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geometric structure using the machinery of BGG sequences. In the locally flat case, this leads to a deformation complex, which generalizes the well known complex for locally conformally...

Integral formulas related to wave fronts

Sergeĭ Anisov (1999)

Banach Center Publications

In the first section of the paper we study some properties of oriented volumes of wave fronts propagating in spaces of constant curvature. In the second section, we generalize to an arbitrary isometric action of a Lie group on a Riemannian manifold the following principle: an extra pression inside of a ball does not move it.

Legendrian and transverse twist knots

John B. Etnyre, Lenhard L. Ng, Vera Vértesi (2013)

Journal of the European Mathematical Society

In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the m ( 5 2 ) knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least n different Legendrian representatives with maximal Thurston-Bennequin number of the twist knot K - 2 n with crossing number 2 n + 1 . In this paper we give a complete classification of Legendrian and transverse representatives of twist knots. In particular, we show that K - 2 n has exactly n 2 2 Legendrian representatives with maximal Thurston–Bennequin...

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